Introducing open-ended problem solving to engage students in mathematical procedures and outcomes.

by Katherine Smith

Grades K-2, Grades 3-5


Traditionally, teaching problem-solving in mathematics includes presenting students with “closed problems” that encourage them to follow a single procedure to reach a single outcome.

I’m moving away from this approach in my class. Instead, I’m encouraging students to approach math problems with many different strategies for reaching a single solution. I’m also asking them to help establish a context for specific mathematical problems so that they can see the real-world application of the math skills they’re developing.

Here’s how I do it:

  • First, I listen closely to students to discover the subjects students are interested in and what they care about.
  • Next, I pose questions asking how they would approach a particular problem and facilitate their research in the interest area.
  • Then, I introduce ways they can apply math skills as part of a related project.

For example: When one student became interested in helping polar bears, I turned this interest into an opportunity for problem solving for the whole class. Through questioning, I was able to lead the students to discovering and solving open-ended mathematical problems related to this real-world project.

Open-ended problem solving is important because kids want to come up with their own ideas when they solve problems. Providing this opportunity makes me feel like a “true teacher.” I’m not giving students answers, sharing procedures, or telling them how to do things. Instead, they’re learning through their own process—one I facilitate by asking questions. And, my whole classroom community benefits: I can more easily give extra time to students who need more foundational, procedural practice and students who are ready to engage more have the opportunity to do so.


What I did well (in sharing this practice with other teachers)…

What I think I did well in sharing this practice with other educators is that I was able to explain the value in moving away from closed math problems to open-ended math problems. In the video, I touched on the importance of making open-ended problem solving available to all students, not just students who are high achieving or gifted, but also on how having an organized step-by-step problem solving board students are able to extend on math topics while the teacher provides additional direct instruction to students who needed more procedural practice. Lastly, I was able to demonstrate how to take a simple problem (2 + 3) and turn it into an open-ended problem with many forms of representation, thus demonstrating the ease and lack of preparation it takes to convert a traditional problem into an open-ended problem.

What I would do more of, better, differently (in sharing this practice again)…

I would include more description of my problem solving board. I would give more explanation and examples of what a riddle, converted word problem and projects look like across mathematical topics and grade levels. For more information on this PLEASE see my resources and powerpoint as there is clear questions to ask yourself and examples of how to convert problems.

In what ways do I still want to learn and grow in using this practice in my classroom…

I would like to continue to learn and grow in the area of open-ended problem solving by continuing to add different project choices across math units covered throughout the school year as well as cross-curricular projects and lessons that incorporate open-ended mathematical

About Katherine Smith

Katherine serves as a 2nd grade teacher at Chime Institute. She has worked at Chime as a special educator in grades K-5 for the past 5 years. Kathe...

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